Question: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 2x + 3$ and $ KL = 7x - 17$ Find $JL$.
A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {2x + 3} = {7x - 17}$ Solve for $x$ $ -5x = -20$ $ x = 4$ Substitute $4$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 2({4}) + 3$ $ KL = 7({4}) - 17$ $ JK = 8 + 3$ $ KL = 28 - 17$ $ JK = 11$ $ KL = 11$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {11} + {11}$ $ JL = 22$